[tex]a_{n} = 2a_{n-1} + 3[/tex]
[tex]a_{1} = 2[/tex]
[tex]a_{2} = 2a_{2-1} + 3 = 2a_{1} + 3 = (2*2) + 3 = 4 + 3 = 7 [/tex]
[tex]a_{3} = 2a_{3-1} + 3 = 2a_{2} + 3 = (2*7) + 3 = 14 + 3 = 17[/tex]
[tex]a_{4} = 2a_{4-1} + 3 = 2a_{3} + 3 = (2*17) + 3 = 34 + 3 = 37[/tex]
[tex]a_{5} = 2a_{5-1} + 3 = 2a_{4} + 3 = (2*37) + 3 = 74 + 3 = 77[/tex]
Hence, the first five terms are 2, 7, 17, 37, 77.
